Overview
- Provides a fairly self-contained introduction to set theory, in particular to the theory of inner models and forcing
- Presents essential aspects of set theory which are required in understanding modern developments of descriptive inner model theory
- Includes proofs of landmark results at the interface of the theory of large cardinals and descriptive set theory
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
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Table of contents (13 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This textbook gives an introduction to axiomatic set theory and examines the prominent questions that are relevant in current research in a manner that is accessible to students. Its main theme is the interplay of large cardinals, inner models, forcing and descriptive set theory.
The following topics are covered:
• Forcing and constructability
• The Solovay-Shelah Theorem i.e. the equiconsistency of ‘every set of reals is Lebesgue measurable’ with one inaccessible cardinal
• Fine structure theory and a modern approach to sharps
• Jensen’s Covering Lemma
• The equivalence of analytic determinacy with sharps
• The theory of extenders and iteration trees
• A proof of projective determinacy from Woodin cardinals.
Set Theory requires only a basic knowledge of mathematical logic and will be suitable for advanced students and researchers.
Reviews
“A book like this is not only useful, it is necessary for set theory. It contains great results, some of the most celebrated in set theory, it finally has a comprehensive exposition of many essential tools … this is the perfect book for someone who already is familiar with set theory, and wants to know more about this specific part. It is also a good introduction for somebody who comes from outside set theory, but is curious about it.” (Vincenzo Dimonte, Studia Logica, Vol. 106, 2018)
“This text is, in its own way, a remarkable accomplishment. While a ‘Universitext’, it somehow manages to pursue a steady path of exposition from the beginnings in the seminal work of Cantor through to Jensen’s covering Lemma and the Martin-Steel Theorem on Projective Determinacy. … this text could well be considered an informative one even for the set theorist.” (A. Kanamori, Mathematical Reviews, June, 2015)
Authors and Affiliations
About the author
Ralf Schindler teaches at Universität Münster and is an expert in the field of set theory.
Ralf Schindler works mostly in the area of descriptive inner model theory. His results are on the construction of inner models and core models, on coding over core models and on applications of inner model theory to descriptive set theory and combinatorics. He isolated the concept of a “remarkable” cardinal.
Bibliographic Information
Book Title: Set Theory
Book Subtitle: Exploring Independence and Truth
Authors: Ralf Schindler
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-319-06725-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2014
Softcover ISBN: 978-3-319-06724-7Published: 06 June 2014
eBook ISBN: 978-3-319-06725-4Published: 22 May 2014
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: X, 332
Number of Illustrations: 10 b/w illustrations